Problem: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 7x - 2$ and $ BC = 6x + 7$ Find $AC$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {7x - 2} = {6x + 7}$ Solve for $x$ $ x = 9$ Substitute $9$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 7({9}) - 2$ $ BC = 6({9}) + 7$ $ AB = 63 - 2$ $ BC = 54 + 7$ $ AB = 61$ $ BC = 61$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {61} + {61}$ $ AC = 122$